How to find out when an equation has no solution

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SAT Math › How to find out when an equation has no solution

Questions 1 - 8

Nosol1

There is no solution

–3

–1/2

Explanation

Nosol2

Solve:

No Solution

Infinitely Many Solutions

$\frac{15}{9}$

Explanation

First, distribute the to the terms inside the parentheses.

Add 6x to both sides.

This is false for any value of . Thus, there is no solution.

Solve $\left | 3-4x\right |<0$ .

No solutions

$x<\frac{4}{3}$

$x>\frac{4}{3}$

$x<\frac{3}{4}$

$x>\frac{3}{4}$

Explanation

By definition, the absolute value of an expression can never be less than 0. Therefore, there are no solutions to the above expression.

Find the solution to the following equation if x = 3:

y = (4x2 - 2)/(9 - x2)

no possible solution

Explanation

Substituting 3 in for x, you will get 0 in the denominator of the fraction. It is not possible to have 0 be the denominator for a fraction so there is no possible solution to this equation.

$\small h\left ( x\right )=\frac{28}{x+4}$

$\small \textup{For which of the following values of},x,\textup{is the above function undefined?}$

$\small -4$

$\small 4$

$\small 0$

$\small 28$

None of the other answers

Explanation

A fraction is considered undefined when the denominator equals 0. Set the denominator equal to zero and solve for the variable.

$\small x+4=0$

$\small x=-4$

Undefined_denom3

I. x = 0

II. x = –1

III. x = 1

I only

II only

III only

II and III only

I, II, and III

Explanation

Undefined_denom2

, Screen shot 2016 02 18 at 9.31.39 am

In the above graphic, approximately determine the x values where the graph is neither increasing or decreasing.

Explanation

We need to find where the graph's slope is approximately zero. There is a straight line between the x values of , and . The other x values have a slope. So our final answer is .